Six balls, numbered 2, 3, 4, 5, 6, 7, are placed in a hat.  Each ball is equally likely to be chosen.  If one ball is chosen, what is the probability that the number on the selected ball is a prime number?
Of the numbers 2, 3, 4, 5, 6, 7, only the numbers 2, 3, 5, and 7 are prime.

Since 4 out of the 6 numbers are prime, then the probability of choosing a ball with a prime number is $\frac{4}{6} = \boxed{\frac{2}{3}}$.